Question

Lydia is concerned that she has strep throat, so she visits her doctor. Base on her initial examination, the doctor believes that there is a 70% chance that Lydia has strep throat. There is a test for strep throat known as the Rapid Strep Test (RST). If an individual has strep throat, the RST correctly identifies this 95% of the time (i.e. the true positive rate is 95%). If an individual does not have strep throat, the RST incorrectly identifies strep 35% of the time (i.e. the false positive rate is 35%).

(a) Suppose that Lydia takes the RST once and the test result comes back positive (i.e. it says she has strep). What is the probability she has strep throat given this result?

(b) Now, suppose that Lydia has experienced adverse side effects with antibiotics in the past, so she wants to be very sure that she has strep throat before beginning to treat it. Instead of doing the RST once, she does it four more times, and she gets back 3 positive test results and 1 negative test result (i.e. three tests says she has strep and one test says she does not have strep). Assume that all tests are independent. What is the probability that Lydia has strep throat given that she has tested positive four times (once from part a and three times from part b) and negative one time?

Answer 1

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